From BCS to the LHC.

*(English)*Zbl 1157.82001The report of the widely-known elementary particle physicist, devoted to the 50th anniversary of the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity, presents a history of fruitful interaction between superconductivity and particle physics. While, there are deep differences in aims and motivations between above scientific directions, however the ideas developed in one field can be very useful in the other. That fruitful idea for particle physics is the idea of spontaneous symmetry breaking following from the BCS theory. All of the dramatic exact properties of superconductors follow from the assumption that electromagnetic gauge invariance is broken. The BCS theory described a mechanism of breaking the electromagnetic gauge invariance, but one derived the properties of superconductors from the BCS dynamical model not from the mere fact of broken symmetry. The phenomenon of spontaneous symmetry breaking produced a revolution in elementary particle physics. The idea of collective excitations in superconductors, being a necessary consequence of the exact gauge invariance, has been introduced by Y. Nambu in particle physics. Together with G. Jona-Lasinio, he developed a theory of spontaneous breaking a chiral symmetry leading to the light pion appearance as a bound state of a nucleon and an antinucleon. The proof that broken exact symmetries always entail exactly massless particles has been obtained in Goldstone-Salam-Weinberg general theorem by using Goldstone bosons. This theorem has found applications in many branches of physics, in particular in cosmology. Then, an exception of the theorem has been found for theories in which the underlying physics is invariant under local symmetries whose transformations can vary from place to place in space and time. P. Higgs, et al. showed that when a local symmetry is spontaneously broken, neither the vector particles with which the symmetry is associated nor the Goldstone bosons produced by the symmetry breaking have zero mass. This discovery based a specific theory which turned out not to be a theory of strong interactions. The mathematical techniques developed in particle physics were used to justify the approximations made by the BCS theory for superconductivity. The spontaneous breaking of the symmetry also yields massive vector particles, the charged W particles and a neutral Z particle experimentally discovered in CERN. For explanation, how is the local electroweak symmetry broken, A. Salam and S. Weinberg introduced elementary scalar fields into the theory, whose vacuum expectation values in the classical approximation would break the symmetry. The elementary scalars appear as physical particles known as Higgs bosons, namely they will be the primary target of the new LHC accelerator in CERN.

Reviewer: I. A. Parinov (Rostov-na-Donu)

##### MSC:

82-03 | History of statistical mechanics |

82D55 | Statistical mechanical studies of superconductors |

01A60 | History of mathematics in the 20th century |

##### Keywords:

BCS theory; superconductivity; elementary particle physics; spontaneous symmetry breaking; history; bosons; LHC
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\textit{S. Weinberg}, Int. J. Mod. Phys. A 23, No. 11, 1627--1635 (2008; Zbl 1157.82001)

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##### References:

[1] | DOI: 10.1103/PhysRev.108.1175 · Zbl 0090.45401 · doi:10.1103/PhysRev.108.1175 |

[2] | Mendelssohn K., The Quest for Absolute Zero (1966) |

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